TAM (version 1.6-0)

data.geiser: Dataset from Geiser et al. (2006)

Description

This is a subsample of the dataset used in Geiser et al. (2006) and Geiser and Eid (2010).

Usage

data(data.geiser)

format

A data frame with 519 observations on the following 24 variables 'data.frame': 519 obs. of 24 variables: $ mrt1 : num 0 0 0 0 0 0 0 0 0 0 ... $ mrt2 : num 0 0 0 0 0 0 0 0 0 0 ... $ mrt3 : num 0 0 0 0 0 0 0 0 1 0 ... $ mrt4 : num 0 0 0 0 0 1 0 0 0 0 ... [...] $ mrt23: num 0 0 0 0 0 0 0 1 0 0 ... $ mrt24: num 0 0 0 0 0 0 0 0 0 0 ...

References

Geiser, C., & Eid, M. (2010). Item-Response-Theorie. In C. Wolf & H. Best (Hrsg.). Handbuch der sozialwissenschaftlichen Datenanalyse (S. 311-332). VS Verlag fuer Sozialwissenschaften. Geiser, C., Lehmann, W., & Eid, M. (2006). Separating rotators from nonrotators in the mental rotations test: A multigroup latent class analysis. Multivariate Behavioral Research, 41(3), 261-293.

Examples

#############################################################################
# EXAMPLE 1: Latent trait and latent class models (Geiser et al., 2006, MBR)
#############################################################################

data(data.geiser)
dat <- data.geiser

#**********************************************
# Model 1: Rasch model
tammodel <- "
  LAVAAN MODEL:
    F =~ 1*mrt1__mrt12
    F ~~ F
  ITEM TYPE:
    ALL(Rasch)
    "
mod1 <- tamaan( tammodel , dat)    
summary(mod1)

#**********************************************
# Model 2: 2PL model
tammodel <- "
  LAVAAN MODEL:
    F =~ mrt1__mrt12
    F ~~ 1*F
    "
mod2 <- tamaan( tammodel , dat)    
summary(mod2)

# model comparison Rasch vs. 2PL
anova(mod1,mod2)

#*********************************************************************
#*** Model 3: Latent class analysis with four classes  

tammodel <- "
ANALYSIS:
  TYPE=LCA;
  NCLASSES(4);   # 4 classes
  NSTARTS(10,20); # 10 random starts with 20 iterations
LAVAAN MODEL:
  F =~ mrt1__mrt12
    "    
mod3 <- tamaan( tammodel , resp=dat  )
summary(mod3)

# extract item response functions
imod2 <- IRT.irfprob(mod3)[,2,]
# plot class specific probabilities
matplot( imod2 , type="o" , pch=1:4 , xlab="Item" , ylab="Probability" )
legend( 10 ,1 , paste0("Class",1:4) , lty=1:4 , col=1:4 , pch=1:4 )

#*********************************************************************
#*** Model 4: Latent class analysis with five classes  

tammodel <- "
ANALYSIS:
  TYPE=LCA;
  NCLASSES(5); 
  NSTARTS(10,20);
LAVAAN MODEL:
  F =~ mrt1__mrt12
    "    
mod4 <- tamaan( tammodel , resp=dat )
summary(mod4)

# compare different models
AIC(mod1); AIC(mod2); AIC(mod3); AIC(mod4)
BIC(mod1); BIC(mod2); BIC(mod3); BIC(mod4)
# more condensed form
IRT.compareModels(mod1, mod2, mod3, mod4)

#############################################################################
# EXAMPLE 2: Rasch model and mixture Rasch model (Geiser & Eid, 2010)
#############################################################################

data(data.geiser)
dat <- data.geiser

#*********************************************************************
#*** Model 1: Rasch model
tammodel <- "
LAVAAN MODEL:
  F =~ mrt1__mrt6
  F ~~ F
ITEM TYPE:
  ALL(Rasch);
    "    
mod1 <- tamaan( tammodel , resp=dat  )
summary(mod1)

#*********************************************************************
#*** Model 2: Mixed Rasch model with two classes
tammodel <- "
ANALYSIS:
  TYPE=MIXTURE ;
  NCLASSES(2);
  NSTARTS(20,25);
LAVAAN MODEL:
  F =~ mrt1__mrt6
  F ~~ F
ITEM TYPE:
  ALL(Rasch);
    "    
mod2 <- tamaan( tammodel , resp=dat  )
summary(mod2)

# plot item parameters
ipars <- mod2$itempartable_MIXTURE[ 1:6 , ]
plot( 1:6 , ipars[,3] , type="o" , ylim=c(-3,2) , pch=16 ,
        xlab="Item" , ylab="Item difficulty")
lines( 1:6 , ipars[,4] , type="l", col=2 , lty=2)
points( 1:6 , ipars[,4] ,  col=2 , pch=2)

#*********************************************************************
#*** Model 3: Mixed Rasch model with three classes
tammodel <- "
ANALYSIS:
  TYPE=MIXTURE ;
  NCLASSES(3);
  NSTARTS(20,25);
LAVAAN MODEL:
  F =~ mrt1__mrt6
  F ~~ F
ITEM TYPE:
  ALL(Rasch);
    "    
mod3 <- tamaan( tammodel , resp=dat  )
summary(mod3)

# plot item parameters
ipars <- mod3$itempartable_MIXTURE[ 1:6 , ]
plot( 1:6 , ipars[,3] , type="o" , ylim=c(-3.7,2) , pch=16 ,
        xlab="Item" , ylab="Item difficulty")
lines( 1:6 , ipars[,4] , type="l", col=2 , lty=2)
points( 1:6 , ipars[,4] ,  col=2 , pch=2)
lines( 1:6 , ipars[,5] , type="l", col=3 , lty=3)
points( 1:6 , ipars[,5] ,  col=3 , pch=17)

# model comparison
IRT.compareModels( mod1 , mod2 , mod3 )